The Law of Reflux Returns

One could make the case, quite convincingly, that all of the major monetary debates are between those whose arguments are based on classical monetary theory and those whose arguments are based on the quantity theory of money. This would be fine if one theory or the other was always correct. However, the model that is appropriate for any given debate depends on the particular monetary institutions in place. For example, if money is convertible into some commodity, such as gold, then classical monetary theory is appropriate. If we have a system of inconvertible paper money, then the quantity theory is appropriate. Thus, to put my original point differently, the history of thought in monetary economics essentially consists of one side using the appropriate model and the other side mis-applying the lessons of the other model.

The quantity theory is perhaps sufficiently well-known that it does not require a long summary. The basic idea is that with a system of inconvertible paper money, the value of that money is determined by the interaction between the supply and demand. An excess supply of money leads to inflation. An excess demand for money leads to deflation. In contrast, under classical monetary theory, the price level is pinned down by the price of gold through arbitrage. The money supply then varies directly with money demand. If banks (or a central bank) issues too many bank notes, then they will experience a wave of redemptions (people start converting their bank notes to gold). This causes a drain of gold reserves and the banks (or central bank) will have to restrict bank note issuance to ensure that they do not lose all of their reserves. (This is known as the Law of Reflux. I will return to this idea later.)

So, if we can summarize this concisely, the quantity theory implies that there can be deviations between the supply of and demand for money that cause price level fluctuations. The classical theory implies that the money supply will move in conjunction with money demand and have no effect on prices.

As I said, a great many of the debates in monetary history involve misapplications of one theory or the other. During the Bullionist Controversy, the British suspended the convertibility of bank notes into gold at the Bank of England. One group, the Bullionists, argued that the subsequent inflation was caused by excess note issuance. The other group, the Anti-Bullionists, argued that this could not be true. In fact, some of the Anti-Bullionists cited Adam Smith as the authority on the topic and argued that it was impossible for an excess supply of money to cause inflation because the money supply only fluctuated with money demand. The Bullionists were essentially applying the quantity theory of money. The Anti-Bullionists were applying the classical theory. As my forthcoming paper in the JMCB shows, the Bullionists were correct. And they were correct because they were applying the correct theory given the circumstances. In fact, if the Anti-Bullionists had read Adam Smith carefully, they would have realized that Adam Smith had assumed a convertible money. They failed to realized that the Law of Reflux does not apply when there is an inconvertible paper money.

The subsequent debate between the Banking School and the Currency School in the U.K. was similarly plagued by misapplications. The Currency School wanted limits on the quantity of notes the Bank of England could issue. The Banking School argued that this was unnecessary, that the Law of Reflux applied. If the Bank of England issued too many notes, they would be converted into gold and the Bank would have to reduce its note issuance. An excess supply of money would not cause inflation. This time it was the Banking School that was correct. Under the gold standard, the quantity theory is not the appropriate framework to apply.

Critics of monetary explanations of the Great Depression like to point to the monetary base and argue that the Fed “did all it could.” However, this mis-applies the Quantity Theory of Money. Economists like Earl Thompson, David Glasner, and Scott Sumner explain that it is more appropriate to look at the gold market for the monetary explanation. Changes in the relative price of gold were the important source of fluctuations in the economy during the early stage of the Depression, 1929 – 1933. In other words, the classical theory is the appropriate framework. (This is complicated by the fact that while the Law of Reflux applies, it is still possible to have an excess demand for money because the central bank has a monopoly over currency issuance and if they fail to increase the money supply, this can cause disruptions in the economy as well. So I view the Thompson-Glasner-Sumner view as the appropriate way to look at the Depression with Friedman and Schwartz as a complement.)

In the 1970s, macroeconomists debated the causes of inflation. On the one side, the Keynesians pointed to the Phillips Curve, which appeared to be a stable negative relationship between the unemployment rate and the inflation rate for an explanation. Specifically, they argued that as labor markets tighten this puts upward pressure on wages, increasing firms costs, and causing higher prices. On the other side of the debate were the Monetarists who argued that the growth rate of the money supply was the source of inflation. The Monetarists were applying the Quantity Theory of Money. The Keynesians meanwhile made a crucial error. What they failed to consider is the data generating process that produced the Phillips Curve. The negative relationship between inflation and unemployment was identified during periods in which money was convertible into gold. Thus, the appropriate model to use to explain these fluctuations is Classical Monetary Theory. According to this view, fluctuations in the gold market were the source of fluctuations in the price level. Such fluctuations were often unexpected. In addition, since prices were relatively constant over long horizons, so were nominal wages. Thus, unexpected fluctuations in the gold market would result in unexpected fluctuations in the price level. With stable nominal wages, this meant that unexpected increases in the price level led to unexpected decreases in real wages and therefore lower unemployment rates. The Keynesian explanation of inflation therefore failed on two fronts: (1) they failed to realize that the relationship might not be robust across monetary regimes, and (2) they reversed the direction of causation in the Phillips Curve. This latter point being an under-appreciated aspect of both Friedman’s and Lucas’s critique of the Phillips Curve.

I bring all of this up because there is once again a debate in monetary economics in which one side is misapplying one of the two theories. This time, it is the Classical Theory that is being misapplied. Specifically, the Law of Reflux is back in vogue. When I discuss paying interest on excess reserves (IOER) and why IOER is contractionary, I am regularly met with the following critique: “the central bank determines the supply of reserves. Individuals banks can try to reduce their reserve balances, but collectively the banking system must hold this supply of reserves.” This is just a modern version of the Law of Reflux. Allow me to explain. The relevant question is not why banks are holding this quantity of reserves. The relevant question is why banks are holding this quantity of excess reserves. It is true that the central bank determines the aggregate quantity supplied of reserves. However, the banking system determines whether these reserves are held as required reserves or as excess reserves. For example, if the bank lends out some of these reserves, they also create a new deposit liability. This new deposit liability increases the amount of required reserves that the bank must hold. If the banking system creates enough new deposits then all of these reserves will be required reserves and banks will not be holding excess reserves (despite the fact that the aggregate supply of reserves is still the same). So when someone says that the banks have no choice but to hold the quantity of reserves the Fed supplies, they must either be (a) confused as to this distinction between aggregate reserves and aggregate excess reserves, or (b) invoking some modern version of the Law of Reflux in which the banking system is unable to convert excess reserves into required reserves.

A better explanation for why banks are holding such a large quantity of excess reserves is not that they have no choice, but rather that they have been given an incentive to do so. In particular, Dutkowsky and VanHoose provide perhaps the most compelling explanation. What they argue is that a good rule of thumb is to compare the interest rate paid on excess reserves to the federal funds rate. If the interest paid on excess reserves is higher than the federal funds rate, then the wholesale market for loans between banks just breaks down. In other words, we should expect to end up in either one or two different corner solutions. In one corner solution, banks hold no excess reserves and engage in wholesale lending. In the other corner solution, banks hold a lot of excess reserves and do not engage in wholesale lending. (It is possible to end up in an interior solution, but only in rare cases.)

As I have written elsewhere, whether or not this matters for monetary policy depends on the monetary transmission mechanism. If you think that monetary policy works solely through the short term nominal rate, then the interest rate paid on excess reserves just replaces the federal funds rate as the relevant policy rate. However, if you think that monetary policy works by altering portfolio composition, including those of banks, then paying IOER actually hinders the monetary transmission mechanism and makes it harder for the central bank to hits its target. (This is incidentally the mechanism Bernanke cited over and over again during rounds of QE.) Regardless, this isn’t the time to revive the Law of Reflux and the implications thereof.

7 responses to “The Law of Reflux Returns”

There are many channels through which money can reflux to its issuer: The gold channel, the bond channel, the loan repayment channel, and the tax channel, to name a few. (Furthermore, convertibility can be instant or delayed, certain or uncertain, costly or costless, at the bank’s initiative or at the customer’s, etc.) If a bank closes ONE of those channels (the gold channel) then it is tempting to call the money inconvertible, but as long as there are other reflux channels available, the money is still convertible. This means that what you call classical monetary theory (and what I call the backing theory, or the real bills doctrine), gives the correct description of how money’s value is determined. To wit: The value of money is determined by the assets and liabilities of the money issuer, exactly the same as the value of stocks, bonds, and every other financial security is determined.

“If the banking system creates enough new deposits then all of these reserves will be required reserves and banks will not be holding excess reserves … A better explanation for why banks are holding such a large quantity of excess reserves is not that they have no choice, but rather that they have been given an incentive to do so.”

Simple observation of the enormous disproportionality between the required reserve ratio and the absurdly enormous deposit expansion that would be required to “use up” trillions in excess reserves makes the first statement utterly inapplicable in any real world sense.

Teeth grinding over the technical difference between funds and IOR is equally irrelevant. There is no incentive. IOR is required to prevent short rates from plummeting to zero. Banks lend if they expect a threshold rate of return over the risk free rate. Concern over a relatively insignificant short rate technical difference is misguided in that context.

The conclusion regarding IOER and FFR comes from the paper by Dutkowsky and VanHoose that I referenced in the post. Their model includes the sort of marginal analysis that you describe in your comment.

“If the banking system creates enough new deposits then all of these reserves will be required reserves and banks will not be holding excess reserves.”

I think you are invoking to ‘money multiplier’ approach for explaining money creation. But The Bank of England explains that this approach is not correct in modern economy. Please correct me if I am wrong. I am confused about it. Here is the paper: